code: def hyperplane_parameters(poly, vertices=None):
      """A helper function to return the hyperplane parameters
      of which the facets of the polytope are a part of.
  
      Parameters
      ==========
  
      poly :
          The input 2/3-Polytope.
      vertices :
          Vertex indices of 3-Polytope.
  
      Examples
      ========
  
      >>> from sympy import Point, Polygon
      >>> from sympy.integrals.intpoly import hyperplane_parameters
      >>> hyperplane_parameters(Polygon(Point(0, 3), Point(5, 3), Point(1, 1)))
      [((0, 1), 3), ((1, -2), -1), ((-2, -1), -3)]
      >>> cube = [[(0, 0, 0), (0, 0, 5), (0, 5, 0), (0, 5, 5), (5, 0, 0),\
                  (5, 0, 5), (5, 5, 0), (5, 5, 5)],\
                  [2, 6, 7, 3], [3, 7, 5, 1], [7, 6, 4, 5], [1, 5, 4, 0],\
                  [3, 1, 0, 2], [0, 4, 6, 2]]
      >>> hyperplane_parameters(cube[1:], cube[0])
      [([0, -1, 0], -5), ([0, 0, -1], -5), ([-1, 0, 0], -5),
      ([0, 1, 0], 0), ([1, 0, 0], 0), ([0, 0, 1], 0)]
      """
      if isinstance(poly, Polygon):
          vertices = list(poly.vertices) + [
              poly.vertices[0]
          ]  # Close the polygon
          params = [None] * (len(vertices) - 1)
  
          for i in range(len(vertices) - 1):
              v1 = vertices[i]
              v2 = vertices[i + 1]
  
              a1 = v1[1] - v2[1]
              a2 = v2[0] - v1[0]
              b = v2[0] * v1[1] - v2[1] * v1[0]
  
              factor = gcd_list([a1, a2, b])
  
              b = S(b) / factor
              a = (S(a1) / factor, S(a2) / factor)
              params[i] = (a, b)
      else:
          params = [None] * len(poly)
          for i, polygon in enumerate(poly):
              v1, v2, v3 = [vertices[vertex] for vertex in polygon[:3]]
              normal = cross_product(v1, v2, v3)
              b = sum([normal[j] * v1[j] for j in range(0, 3)])
              fac = gcd_list(normal)
              if fac.is_zero:
                  fac = 1
              normal = [j / fac for j in normal]
              b = b / fac
              params[i] = (normal, b)
      return params
  
imports: from functools import cmp_to_key
  from sympy.abc import x, y, z
  from sympy.core import S, diff, Expr, Symbol
  from sympy.core.sympify import _sympify
  from sympy.geometry import Segment2D, Polygon, Point, Point2D
  from sympy.polys.polytools import LC, gcd_list, degree_list, Poly
  from sympy.simplify.simplify import nsimplify
label_desc: Use image node_id 14 for calling a global function with example usage: hyperplane_parameters(poly, vertices) and returns: params